{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1c2e4e66",
   "metadata": {},
   "source": [
    "# Распределения на дела "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cda69b59",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as sps\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "from collections import Counter\n",
    "from collections import OrderedDict\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "135429ab",
   "metadata": {},
   "source": [
    "## 1. Биномиальное распределение"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fa54b9e",
   "metadata": {},
   "source": [
    "<strong>Предыстория:</strong> когда-то в лет 15-16 я услышал следующий вопрос: \"если выпадет орел 100 раз подряд, то с какой вероятностью выпадет орел в 101 раз\". Я ответил: \"с очень низкой, так как он уже выпал до этого 100 раз\", однако, это непрада, так как события независимы и вероятность равна 0.5. Все моё нутро кричало об обратном, но здравый смысл победил. В дальнейшем, я осознал что изначально неверно воспринимал вероятности и их связь с распределением случайной величины. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cb5280d",
   "metadata": {},
   "source": [
    "<strong>Биномиальное распределение - </strong>распределение количества «успехов» в последовательности из \n",
    "N независимых случайных экспериментов, таких, что вероятность «успеха» в каждом из них постоянна и равна p. Где $p$ - вероятность одного благоприятного события, а $p - 1$ вероятность одного неудачного эксперимента.\n",
    "\n",
    "<strong>Пример:</strong> независимо подбрасываем N монет, может выпасть исключительно одно из следующих событий { 'Орел', 'Решка' }. Нас интересует количество событий { 'Орел' } из всех проведенных экспериментов."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "aea10dbc",
   "metadata": {},
   "outputs": [],
   "source": [
    "Ω = [ 'Орел', 'Решка' ] # множество элементарных событий\n",
    "A = [ 'Орел' ] # благоприятное событие\n",
    "\n",
    "N = 100 # количество экспериментов\n",
    "D = 2000 # количество индервалов для деления\n",
    "flips = 100 # количество подбрасываний монеток в каждом эксперименте\n",
    "P = len(A) / len(Ω) # вероятность события { 'Орел' }\n",
    "\n",
    "o = 10 ** -5 # маленькое число, нужно для отрисовки интервалов #### Искусственный пример"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1eb6b09f",
   "metadata": {},
   "source": [
    "#### Искусственный пример"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5e250d7e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def experimental(n = N, dist = D, color = 'yellow'):\n",
    "    interval = np.arange(dist)\n",
    "    binomial = sps.binom.pmf(interval, n, P)\n",
    "    \n",
    "    plt.bar(interval, binomial)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7ad5c206",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "experimental(N, D)\n",
    "plt.xlim([\n",
    "    sps.binom.ppf(o, N, P), \n",
    "    sps.binom.ppf(1 - o, N, P)\n",
    "])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40c238f6",
   "metadata": {},
   "source": [
    "#### Практический пример"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4e89599b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate(N):\n",
    "    values = []\n",
    "\n",
    "    for i in range(N):\n",
    "        value = random.choices(Ω, k = flips).count(A[0])\n",
    "        values.append(value)\n",
    "    \n",
    "    return np.array(values)\n",
    "\n",
    "def practical(repeats):\n",
    "    \n",
    "    values = np.arange(repeats)\n",
    "    probabilities = generate(repeats)\n",
    "    \n",
    "    dictionary = dict.fromkeys(values, 0)\n",
    "    \n",
    "    for i in probabilities:\n",
    "        dictionary[int(i)] += 1 / repeats\n",
    "    \n",
    "    return dictionary.keys(), np.array(list(dictionary.values()))\n",
    "\n",
    "def add_graph(repeats, color):\n",
    "    \n",
    "    values, probabilities = practical(repeats)\n",
    "    \n",
    "    plt.plot(values, probabilities, color = color)\n",
    "    \n",
    "    return values, probabilities"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cd904e2",
   "metadata": {},
   "source": [
    "Покажем на одном графике искусственный и практические примеры. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "995e4c34",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "add_graph(100, color = 'red')\n",
    "add_graph(2_000, color = 'green')\n",
    "add_graph(50_000, color = 'blue')\n",
    "\n",
    "experimental(N, D)\n",
    "\n",
    "# устанавливаем интервал отрисовки по крайним значениями\n",
    "# теоретического биномиального распределения\n",
    "plt.xlim([\n",
    "    sps.binom.ppf(o, N, P), \n",
    "    sps.binom.ppf(1 - o, N, P)\n",
    "])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a37bb8bd",
   "metadata": {},
   "source": [
    "Как мы видим, чем больше выборка в практическом варианте, тем ближе она к теоретическому примеру."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0122d55c",
   "metadata": {},
   "source": [
    "#### Биномиальный тест\n",
    "\n",
    "Проведем проверку, что вероятность успеха равна $P$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91e5929b",
   "metadata": {},
   "source": [
    "1. Количество всех благоприятных исходов\n",
    "2. Количество экспериментов\n",
    "3. Ожидаемая вероятность"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "78697295",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BinomTestResult(k=50, n=100, alternative='two-sided', statistic=0.5, pvalue=1.0)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sps.binomtest(50, flips, 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53258d7f",
   "metadata": {},
   "source": [
    "То есть, вероятность того, что из flips подбрасываний, выпадет 50 орлов равна 0.5 с вероятностью $p-value = 1$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a4b253ec",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BinomTestResult(k=5054, n=10000, alternative='two-sided', statistic=0.5054, pvalue=0.2846187276368312)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sps.binomtest(sum(generate(N)), N * flips, P)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acb5db41",
   "metadata": {},
   "source": [
    "$p-value > 0.05$, следовательно у нас хорошие шансы на то, что у нас правильно задана $P$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4edb1c0",
   "metadata": {},
   "source": [
    "#### Важная идея (<a href=\"https://habr.com/ru/articles/730936/\">источник</a>)\n",
    "\n",
    "Графики, которые мы получили очень похожи на нормальное распределение, по сути, нормальное распределение это предельный случай биномиального распределения.\n",
    "Случайная величина, которая следует <strong>распределению Бернулли</strong>, может принимать только два возможных значения, но случайная величина, которая следует <strong>биномиальному распределению</strong>, может принимать несколько значений.\n",
    "\n",
    "Предположим, у нас есть последовательность испытаний Бернулли, каждое с вероятностью успеха p, и мы повторяем этот эксперимент n раз. Пусть X — количество успехов в n испытаниях. Тогда X  имеет биномиальное распределение с параметрами n, p. Функция массы вероятности X  определяется как:\n",
    "\n",
    "\\begin{equation} P(X=k) = \\binom{n}{k}p^k(1-p)^{n-k} \\end{equation}\n",
    "Самая тяжелая часть — факториал. Давайте воспользуемся приближением Cтирлинга, чтобы вычислить факториалы быстрее:\n",
    "\n",
    "\\begin{equation} n! \\approx n^n e^{-n} \\sqrt{2\\pi n}= \\sqrt{2\\pi n}(\\frac{n}{e})^n \\end{equation}\n",
    "Подставив это в Биномиальный коэффициент мы получаем:\n",
    "\n",
    "\\begin{align} \\frac{n!}{k!(n-k)!} \\approx \\frac{\\sqrt{2\\pi n}(\\frac{n}{e})^n}{\\sqrt{2\\pi k}(\\frac{k}{e})^k \\sqrt{2\\pi (n-k)}(\\frac{n-k}{e})^{n-k}}   \\end{align}\n",
    "Это может выглядеть пугающе, но на самом деле это просто замена и некоторая перестановка терминов.\n",
    "\n",
    "Подставляя это приближение в PMF Биномиального распределения, мы получаем:\n",
    "\n",
    "\\begin{align} P(X=k) = \\binom{n}{k}p^k(1-p)^{n-k} \\approx \\frac{1}{\\sqrt{2\\pi n p (1-p)}} \\cdot \\exp\\left(-\\frac{(k-np)^2}{2np(1-p)}\\right) \\end{align}\n",
    "Это функция плотности вероятности нормального распределения при $\\mu = np$, и квадратом $\\sigma^2 = np(1-p)$:\n",
    "\n",
    "\\begin{equation} f(x) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left(-\\frac{(x-\\mu)^2}{2\\sigma^2}\\right) \\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94c56c2b",
   "metadata": {},
   "source": [
    "## 2. Распределение Пуассона "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42c4e71f",
   "metadata": {},
   "source": [
    "<strong>Предыстория:</strong> я листал TikTok и увидел что на MacOS в папке `/System/Library/Image\\ Capture/Devices/VirtualScanner.app/Contents/Resources/simpledoc.pdf` есть Bitcoin White Paper, этот документ открыт в интернете и так, поэтому не так важно что я его нашел, а то что я его впервые открыл и прочитал, на волне интереса к разработке Smart контраков на Solidity. На 7 странице я увидел применение распределения Пуассона для оценки вероятности успеха взлома сети, поэтому интересно!  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52f7be9d",
   "metadata": {},
   "source": [
    "<strong>Распределение Пуассона</strong> - распределение дискретного типа случайной величины, представляющей собой число событий, произошедших за фиксированное время, при условии, что данные события происходят с некоторой фиксированной средней интенсивностью и независимо друг от друга.\n",
    "\n",
    "Распределение Пуассона играет ключевую роль в теории массового обслуживания."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c099816",
   "metadata": {},
   "source": [
    "<strong>Отличие от биномиального</strong> заключается в том, что у нас нет фиксированного числа экспериментов, а только количество событий за интервал времени."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a1ac896",
   "metadata": {},
   "source": [
    "<strong>Пример:</strong>\n",
    "Задача злоумышленника сделать свой blockchain основным, но для этого нужно первым считать 0x000... хэши для следующих блоков в главной цепи и обманывать остальных. Даже если он сможет сделать это один раз, при подсчете следующего блока ему тоже нужно быть первым, иначе blockchain откатится обратно на один и придется начинать сначала. Поэтому, если он хочет добиться своей конечной цели, то ему следует захватить большую часть сети, что допускается как невозможный сценарий в BitCoin. \n",
    "Посчитаем, как далеко сможет продвинуться злоумышленник если:\n",
    "$p$ - шанс того, что верная цепь посчитает следующий блок\n",
    "$q$ - аналогично, только, цепь - злоумышленника\n",
    "$z$ - номер блока\n",
    "\n",
    "$λ$ - среднее количество событий за фиксированный промежуток времени. То есть, если промежуток вычисления блоков увеличился, то и $λ$ пропорционально растет $z$, а $p$ и $q$ взаимоисключающие события, поэтому нас интересует количество блоков, подсчитанных злоумышленником.\n",
    "\n",
    "$λ = z * \\frac{q}{p}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4213ea8",
   "metadata": {},
   "source": [
    "Постороим график плотности распределени Пуассона для следующего случая, злоумышленник захватил почти всю сеть и имеет вероятность получить хэш первым 49%, более того, он первым посчитал следующие 20 блоков."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4b935429",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "values = np.arange(0, 100)\n",
    "\n",
    "q = 0.49\n",
    "p = 1 - q\n",
    "z = 20\n",
    "\n",
    "λ = z * q / p\n",
    "\n",
    "plt.plot(values, sps.poisson(λ).pmf(values))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3eec6b91",
   "metadata": {},
   "source": [
    "Вероятность того, что злоумышленник протянет еще 20 блоков крайне мала, покажем экспоненциально падающую вероятность на графиках"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7b480f86",
   "metadata": {},
   "outputs": [],
   "source": [
    "def attacker_success_probability(q, z):\n",
    "    p = 1.0 - q\n",
    "    λ = z * (q / p)\n",
    "    \n",
    "    total = 1.0\n",
    "    \n",
    "    for k in range(z + 1):\n",
    "        poisson = np.exp(-λ)\n",
    "        for i in range(1, k + 1):\n",
    "            poisson *= λ / i\n",
    "        total -= poisson * (1 - np.power(q / p, z - k));\n",
    "        \n",
    "    return total\n",
    "\n",
    "def add_to_graph(q):\n",
    "    probabilities = list(map(lambda x: attacker_success_probability(q, x), values))\n",
    "    plt.plot(values, probabilities, label = f'q = {q}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1306805",
   "metadata": {},
   "source": [
    "Выведем графики для вероятностей в зависимости количества блоков"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "36050696",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(4):\n",
    "    add_to_graph((i + 1) / 10)\n",
    "    \n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4aaf2d14",
   "metadata": {},
   "source": [
    "<strong>Вывод:</strong> как мы видим, шанс такого развития событий экспоненциально падает, поэтому при достаточно малом количестве peer, blockchain можно считать защищенным от такого типа атаки."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
